Information on Result #682113
Linear OA(5110, 1953145, F5, 15) (dual of [1953145, 1953035, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,6]) based on
- linear OA(5109, 1953126, F5, 15) (dual of [1953126, 1953017, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(591, 1953126, F5, 13) (dual of [1953126, 1953035, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(51, 19, F5, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(5110, 1027868, F5, 2, 15) (dual of [(1027868, 2), 2055626, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5110, 1027868, F5, 3, 15) (dual of [(1027868, 3), 3083494, 16]-NRT-code) | [i] | ||
| 3 | Digital (95, 110, 1027868)-net over F5 | [i] | ||
| 4 | Linear OOA(5110, 651048, F5, 3, 15) (dual of [(651048, 3), 1953034, 16]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5110, 279020, F5, 15, 15) (dual of [(279020, 15), 4185190, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |